Oct/Nov 2020

Which quantity counts as a physical quantity?

Physical quantities

The diagram gives the masses and velocities of two trolleys that are just about to collide. Following the collision, they travel away together. What is the kinetic energy lost during the collision?

Linear momentum and its conservation

A particle is initially stationary between two metal plates X and Y. A potential difference (p.d.) is then applied across the plates, creating the electric field shown. When the p.d. is applied, the particle moves towards plate X. What could be the particle?

Potential difference and power

To open a vertical gate, two people push on it. The diagram shows the forces each person applies to the gate. One person is a distance $d_1$ from the hinge of the gate and applies a horizontal force $F_1$ at an angle $\theta_1$ to the gate. The other person is a distance $d_2$ from the hinge and applies a horizontal force $F_2$ at an angle $\theta_2$ to the gate. What is the combined moment about the hinge produced by forces $F_1$ and $F_2$?

Turning effects of forces

A ball moves down a slope at a constant speed. The three forces acting on the ball are its weight, the contact force normal to the slope and friction. Which diagram could show these three forces?

Equilibrium of forces

One arm of a U-shaped tube is connected to a gas tap, while the opposite arm is open to the air. The tube contains water with density $1000\ \text{kg m}^{-3}$, and the heights of the water level in both arms are indicated. Atmospheric pressure is $101\ \text{kPa}$. What is the pressure of the gas at the gas tap?

Density and pressure

A trolley moves from P to Q along a track. When it reaches Q, its potential energy is $50\ \text{kJ}$ less than it is at P. At P, the trolley has a kinetic energy of $5\ \text{kJ}$. As it travels from P to Q, it does $10\ \text{kJ}$ of work against friction. What is the kinetic energy of the trolley at Q?

Gravitational potential energy and kinetic energy

A hydroelectric power station converts the gravitational potential energy of water into electrical energy. In one specific power station, the mass of water passing per unit time is $1.5 \times 10^5\ \text{kg s}^{-1}$. The water descends through a vertical drop of $120\ \text{m}$. The electrical power output is $100\ \text{MW}$. Calculate the efficiency of the power station?

Gravitational potential energy and kinetic energy

Which energy value is not $2400\ \text{J}$?

SI units

A train of mass $300\ 000\ \text{kg}$ is speeding up at $0.80\ \text{m s}^{-2}$. At a certain moment, the train is moving at $5.0\ \text{m s}^{-1}$ and the resistive force opposing its motion is $15\ \text{kN}$. At this moment, what is the rate at which the kinetic energy of the train is increasing?

Gravitational potential energy and kinetic energy

A wire with a circular cross-section that obeys Hooke’s law is used to support a basket, as illustrated. The Young modulus of the wire’s material is $2.5 \times 10^{11}\ \text{Pa}$. When an additional load of $34\ \text{N}$ is placed in the basket, the strain in the wire rises by $6.0 \times 10^{-5}$. What is the radius of the wire?

Stress and strain

Which time interval has the smallest duration?

Physical quantities

A rubber cord that is not stretched is pulled by a force $F$. A graph is drawn of force $F$ against extension $x$. $F$ is then raised gradually from zero, so the cord extends along path P. After that, $F$ is lowered again to zero along path Q. What does the shaded area represent?

Elastic and plastic behaviour

A guitar string is set into vibration so that it produces a sound. The wave speed in the guitar string is always $440\ \text{m s}^{-1}$. The vibrating string also generates a sound wave that travels through the air at a speed of $330\ \text{m s}^{-1}$. Which graph shows how frequency $f$ changes with wavelength $\lambda$ for the waves in the string and in the air?

Progressive waves

The graph illustrates how displacement changes over time for two different waves, X and Y. Wave X has frequency $f$ and amplitude $A$. What are the frequency and the amplitude of wave Y?

Progressive waves

A loudspeaker sends a sound wave into a tube that is at first completely filled with water. A tap at the base of the tube is then opened, allowing the water to drain away slowly. At certain air-column lengths in the tube, the sound that is heard becomes much louder. The first loud sound occurs when the air column in the tube is of length $x$. The next loud sound occurs when the air column in the tube is of length $y$. What is the wavelength of the sound wave from the loudspeaker?

Stationary waves

A source producing sound at a frequency of $1000\ \text{Hz}$ moves directly towards a stationary observer. The observer records the frequency of the sound received as $1500\ \text{Hz}$. The speed of sound in still air is $330\ \text{m s}^{-1}$. What is the speed of the source of sound?

Doppler effect for sound waves

The graph illustrates how the intensity of electromagnetic radiation from a distant star changes with wavelength. In which part of the electromagnetic spectrum is the radiation intensity greatest?

Electromagnetic spectrum

Which statement about a stationary wave is correct?

Stationary waves

Which waves would provide the best demonstration of diffraction through a doorway?

Diffraction

Two loudspeakers are positioned close together and are directed in the same direction. A microphone linked to an oscilloscope is then moved along a line at some distance from the loudspeakers, as illustrated. Which statement about the waves produced by the loudspeakers is not a necessary condition for the microphone to find a fixed point on the line where no sound is heard?

Interference

A parallel beam of white light is incident on a diffraction grating. Orange light with wavelength $600\ \text{nm}$ in the fourth-order diffraction maximum overlaps with blue light in the fifth-order diffraction maximum. Determine the wavelength of the blue light.

The diffraction grating

P and R are coplanar vectors. If $X = P - R$, which diagram shows vector $X$ most accurately?

Scalars and vectors

The diagram illustrates the electric field close to a positively charged sphere and a negatively charged sphere. Four electrons A, B, C and D are marked at different locations in the field. For which electron is the direction of the force on the electron indicated correctly?

Scalars and vectors

An oil drop of mass $m$ carries charge $q$. It is kept at rest in an electric field between two parallel horizontal plates separated by distance $d$, as illustrated. The potential difference across the plates is $V$ and the acceleration due to free fall is $g$. What is the charge-to-mass ratio $\frac{q}{m}$ for the oil drop?

Potential difference and power

In copper wire X, which has radius $5.0 \times 10^{-5}\,\text{m}$, free electrons move along the wire with an average drift speed of $2.8 \times 10^{-2}\,\text{m s}^{-1}$. The current in this wire is $3.0\,\text{A}$. Copper wire Y has a current of $2.0\,\text{A}$ and a radius of $1.0 \times 10^{-4}\,\text{m}$. What is the average drift speed of the free electrons in copper wire Y?

Electric current

What does the term potential difference mean?

Potential difference and power

A cable of total length $L$, made up of two wires, connects a $12.0\,\text{V}$ power supply with negligible internal resistance to a lamp, as illustrated. The potential difference across the lamp is $10.5\,\text{V}$. The current in the wire is $2.50\,\text{A}$. Each wire is constructed from metal of resistivity $1.70 \times 10^{-8}\,\Omega\,\text{m}$ and has a cross-sectional area of $6.00 \times 10^{-7}\,\text{m}^2$. What is the value of the length $L$ of the cable?

Resistance and resistivity

In the circuits shown, the power supply has an electromotive force (e.m.f.) that is greater than the lamp’s normal operating voltage. The power supply’s internal resistance is negligible. The variable resistor is varied from zero up to its maximum resistance. In which circuit could the voltage across the lamp increase from zero to its normal operating voltage without going above its normal operating voltage?

Potential dividers

Three identical lamps $L_1$, $L_2$ and $L_3$ are connected to a battery with negligible internal resistance, as shown in the diagram. What change occurs in the brightness of lamps $L_1$ and $L_2$ when switch $S$ is closed?

Practical circuits

For the circuit illustrated, the $6.0\,\text{V}$ battery is assumed to have negligible internal resistance. The resistors $R_1$ and $R_2$, together with the voltmeter, each have a resistance of $100\,\text{k}\Omega$. What current flows in resistor $R_2$?

Practical circuits

Which statement concerning two nuclei that are isotopes of the same element is correct?

Atoms, nuclei and radiation

In a nuclear physics experiment, a nucleus of $^{32}_{16}\text{S}$ strikes a nucleus of $^{94}_{42}\text{Mo}$. The two nuclei fuse and then instantly produce one alpha-particle. The nuclear reaction is shown below. $^{32}_{16}\text{S} + ^{94}_{42}\text{Mo} \rightarrow X + \alpha$ What is nucleus $X$?

Atoms, nuclei and radiation

A student employs a cathode-ray oscilloscope (CRO) to determine the period of a signal. She adjusts the CRO time-base to $5\ \text{ms cm}^{-1}$ and views the trace shown below. The trace measures $10.0\ \text{cm}$ in length. What is the period of the signal?

Practical circuits

Which diagram shows the quark composition of an antineutron?

Atoms, nuclei and radiation

A spherical golf ball has its diameter determined with calipers as $(4.11 \pm 0.01)\ \text{cm}$. For a sphere, the volume is $V = \frac{1}{6}\pi d^{3}$, where $d$ represents the sphere’s diameter. What is the volume of the golf ball?

Errors and uncertainties

A student rides a bicycle uphill from home to a shop, and this takes $10$ minutes. The student then remains in the shop for $5$ minutes, before cycling back home downhill at twice the original speed. Which graph could represent how the cyclist’s distance travelled changes with time?

Non-uniform motion

Two cars X and Y move along the same straight road. Car X moves with a steady speed of $6.0\ \text{m s}^{-1}$. Car Y has a steady acceleration of $0.50\ \text{m s}^{-2}$. At the instant shown, car X is ahead of car Y by a distance $d$. Car Y is moving at a speed of $4.0\ \text{m s}^{-1}$. After $20$ seconds, car Y is level with car X. What is the distance $d$?

Equations of motion

The graph illustrates how quantity P changes with quantity Q for an object that has been falling through air for a long period in a uniform gravitational field. What might P and Q represent?

Non-uniform motion

A rock R, with mass $1.0 \times 10^{27}\ \text{kg}$, is far from a star S and is moving at a speed of $1.0 \times 10^{4}\ \text{m s}^{-1}$. The star has mass $1.0 \times 10^{30}\ \text{kg}$. The rock moves round the star along the path shown, causing it to reverse the direction of its motion and, when it is once more far from the star, to have the same speed as at the start. Which statement is correct?

Gravitational potential energy and kinetic energy

A student measures the volume of a metal coin to find the metal’s density. Which piece of information is not required to estimate the coin’s volume?

Density and pressure

Two balls, with masses $2m$ and $m$, undergo a collision. The diagrams display the balls’ velocities before and after the collision. Which collision is not elastic?

Linear momentum and its conservation

The diagram depicts a ‘ballistic pendulum’. A pellet of mass $m$ moving with speed $u$ strikes a block of mass $M$ that is initially at rest. The pellet becomes lodged in the block and makes the block move with speed $v$ immediately after the collision. If a pellet of mass $2m$, moving with speed $2u$, strikes a block of mass $2M$, what is the speed of the block immediately after the collision? (Ignore the slight increase in the mass of the block as the pellet’s mass is added during the collision.)

Linear momentum and its conservation

A rigid circular disc, with radius $r$, is centred at $X$. Several forces, each of magnitude $F$, are applied at the rim of the disc. Every force lies in the plane of the disc. Which arrangement of forces gives a resultant moment with magnitude $2Fr$ about $X$?

Turning effects of forces

The diagram represents a uniform beam $PQ$. Its length is $3.0\,\text{m}$ and its weight is $50\,\text{N}$. The beam rests on a pivot that is $1.0\,\text{m}$ from end $P$. A load with weight $W$ is attached at end $P$. The beam is balanced in equilibrium. What is the value of $W$?

Equilibrium of forces

During a high-wire circus performance, a man with mass $85\,\text{kg}$ is stationary at the centre of the wire. On both sides of the man, the wire makes an angle of $20^{\circ}$ to the horizontal. What is the tension $T$ in the wire?

Equilibrium of forces

An ice block in the shape of a cylinder has cross-sectional area $12\,\text{m}^2$ and is floating in the sea, with part of it below the surface. The sea water has density $1020\,\text{kg m}^{-3}$. A polar bear with mass $400\,\text{kg}$ climbs onto the ice block. As a result, the block moves downward by a vertical distance $d$. What is the value of $d$?

Density and pressure

A ball is projected vertically upwards. Air resistance may be ignored. Which statement is correct?

Equations of motion

A hammer that has $10\,\text{J}$ of kinetic energy strikes a nail and drives it $5.0\,\text{mm}$ into a plank. After the collision, both the hammer and the nail are at rest. What is the approximate average force acting on the nail as it travels through $5.0\,\text{mm}$?

Energy conservation

For an object of mass $m$ moving through height $\Delta h$ close to the Earth’s surface, the change in gravitational potential energy $\Delta E$ is represented by the equation below. $\Delta E = mg\Delta h$ Which equation is required to derive this expression?

Gravitational potential energy and kinetic energy

A racing car produces an output power of $300\,\text{kW}$ while moving at a steady speed of $60\,\text{m s}^{-1}$. Determine the total resistive force acting on the car.

Energy conservation

The speed $v$ of waves on a stretched wire is represented by $v = T^p \mu^q$ where $T$ denotes the tension in the wire and $\mu$ denotes the mass per unit length of the wire. Determine the values of $p$ and $q$.

Progressive waves

A $60.0\,\text{g}$ mass is hung from a spring, and the measured distance from the bottom of the spring to the floor is $16.4\,\text{cm}$. The mass is then changed to a $100.0\,\text{g}$ mass, and the new distance from the bottom of the spring to the floor is $12.6\,\text{cm}$. The spring obeys Hooke’s law. What is the spring constant of the spring?

Elastic and plastic behaviour

The graph depicts the force-extension graph for a wire. The wire is already extended by a force of $60\,\text{N}$. How much work is required to increase the extension of the wire by $2.0\,\text{mm}$?

Elastic and plastic behaviour

The speed $v$ of waves in deep water is related by the equation $v^2 = \frac{g\lambda}{2\pi}$ where $\lambda$ represents the wavelength of the waves and $g$ represents the acceleration of free fall. A student measures the wavelength $\lambda$ and the frequency $f$ for a number of these waves. Which graph should he plot so that the graph is a straight line through the origin?

Progressive waves

As sound passes through air, the air particles oscillate. The displacement-time graph for one air particle is given. Which graph shows the way the kinetic energy of the air particle changes with time?

Progressive waves

A vibrating tuning fork is placed above a glass cylinder that is filled to the top with water. The water level is then lowered steadily. The first loud sound is produced when the water level is $83.5\,\text{cm}$ above the bench. The following loud sound is produced when the water level is $17.1\,\text{cm}$ above the bench. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the frequency of the tuning fork?

Stationary waves

An emergency vehicle is emitting its siren while it speeds up on a straight road between points $X$ and $Y$, as shown in the diagram. The siren produces a sound frequency of $750\,\text{Hz}$. One person is positioned at $X$ and another person is positioned at $Y$. What describes the sounds heard by the people at $X$ and at $Y$ as the vehicle accelerates?

Doppler effect for sound waves

A section of the electromagnetic spectrum is displayed. What is the name of the shaded region, and what is the order of magnitude of a wavelength of a wave from this region?

Electromagnetic spectrum

In each diagram, the three waves have the same amplitude and frequency, but their phase is different. When they are combined, they form a resultant wave. For which situation is the resultant wave zero at this instant?

Interference

A transmitting mast emits microwaves with wavelength $1.5\,\text{cm}$ and radio waves with wavelength $1.5\,\text{km}$. A receiving aerial located behind a mountain can pick up the radio waves, but it cannot detect the microwaves. What is the reason for this?

Diffraction

A demonstration of double-slit interference is set up with light of wavelength $500\,\text{nm}$. The spacing between neighbouring bright fringes in the interference pattern is $5\,\text{mm}$. What could the values be for the distance from the slits to the screen, and for the slit separation?

Interference

The diagram represents a force $F$. $P$ is the horizontal component of $F$, with $\theta$ being the angle between $P$ and $F$. Which graph most clearly shows how the magnitude of $P$ varies with $\theta$?

Scalars and vectors

Monochromatic light is directed onto a diffraction grating. Seven bright spots are seen on a screen. Which change would increase the number of bright spots observed?

The diffraction grating

A molecule may act as an electric dipole, made up of two point charges of equal magnitude and opposite sign, with a constant separation between them. As shown, the molecule enters a vertical uniform electric field while moving with steady horizontal velocity. The molecule’s positive and negative charges enter the field simultaneously. What is the effect of the electric field on the velocity of the molecule?

Momentum and Newton's laws of motion

A battery with negligible internal resistance is connected to two parallel metal plates. One plate is then brought slowly nearer to the other. Which row is correct?

Potential difference and power

At the rim of an insulating disc of radius $r$, four point charges, each with charge $Q$, are situated. The disc turns at a rate of $n$ revolutions per unit time. What is the equivalent electric current at the rim of the disc?

Electric current

In the circuit diagram, a fixed resistor $X$ is connected in series with a battery and a variable resistor. When a current of $3.0\,\text{A}$ flows through resistor $X$, the power dissipated in it is $7.2\,\text{W}$. The variable resistor is then altered so that the power dissipated in $X$ rises by $50\%$. What is the new current in the circuit?

Potential difference and power

A resistor and a filament lamp are connected in series to a power supply. The $I\text{-}V$ characteristics for the resistor and the lamp are shown. The potential difference (p.d.) across the resistor is $3.3\,\text{V}$. What is the resistance of the lamp?

Resistance and resistivity

A car battery has an electromotive force (e.m.f.) of $12\,\text{V}$ and an internal resistance of $0.05\,\Omega$. It is linked to the starter motor of a car, and the current in the motor is $160\,\text{A}$. What is the terminal p.d. across the battery?

Potential difference and power

A cell with negligible internal resistance is joined to a resistor network and a voltmeter, as shown. The voltmeter gives a reading of zero. What is the value of the resistance of resistor $R$?

Potential dividers

A voltmeter is connected in the circuit with the polarity shown in the diagram. The sliding contact is moved first to end P of the potentiometer and then to end Q. What are the two readings on the voltmeter?

Potential dividers

What conclusion can be drawn from the alpha-particle scattering experiment?

Atoms, nuclei and radiation

A student wants to measure a length of about $10\,\text{cm}$ with a precision of $0.01\,\text{cm}$. Which measuring instrument should be used?

Errors and uncertainties

Which particle is classified as a hadron?

Fundamental particles

A steel ball is released and drops through a vertical distance $h$. The time $t$ for the drop is recorded using light gates. The data are shown in the table: $h = (4.05 \pm 0.01)\,\text{m}$, $t = (0.91 \pm 0.02)\,\text{s}$. The acceleration of free fall $g$ is determined from the equation shown below. $h = \frac{1}{2} g t^2$ What percentage uncertainty is there in the value of $g$?

Errors and uncertainties

A stone is projected straight upwards from point $X$ at time $t = 0$. The graph shows how the velocity $v$ of the stone changes with time $t$. What is the displacement of the stone from point $X$ at time $t = 3.0\,\text{s}$?

Equations of motion

A $5.0\,\text{kg}$ mass is let go from rest on a surface with no friction that is inclined at $30^\circ$ to the horizontal. Air resistance can be ignored. What distance does the mass cover in a time of $0.80\,\text{s}$?

Equations of motion

Which option is not a statement of one of Newton’s laws of motion?

Momentum and Newton's laws of motion

An object drops from a high building. The graph indicates how the object's velocity varies with time $t$. The acceleration due to free fall is $g$. Which statement describes the object's acceleration at times $t = Y$ and $t = Z$?

Equations of motion

What would be a sensible estimate for the volume of a standard football when it is fully inflated?

Physical quantities

An object of mass $m$ moving at speed $5u$ runs into an object of mass $5m$ that is travelling in the same direction at speed $u$, and the two objects stick together. What is the speed at which they move together in the original direction?

Linear momentum and its conservation

A bubble of air is moving upwards through a liquid at a steady speed. The forces acting on it are the upthrust $U$, the viscous drag $V$ and its weight $W$. Which diagram shows the directions and relative magnitudes of the forces?

Equilibrium of forces

A couple exerts a clockwise torque of $9.0\,\text{N m}$ on a circular disc. Which diagram represents this couple?

Turning effects of forces

A shelf PQ is fixed to a vertical wall at P and carries a book. A rigid bar XY keeps the shelf level, as shown. The shelf has weight $W_s$ and the book has weight $W_b$. The bar makes an angle $\theta$ with the shelf and applies a force $F$ to the shelf. The shelf is in equilibrium. What are the magnitudes of the horizontal and the vertical components of the force exerted by the wall on the shelf at P?

Equilibrium of forces

A glider is moving downwards at a steady speed at an angle of $15^{\circ}$ to the horizontal. The diagram shows the directions of the lift $L$, air resistance $R$ and weight $W$ that act on the glider. Which vector triangle could show the forces acting on the glider?

Equilibrium of forces

A solid cylinder with density $\rho_c$, cross-sectional area $A$ and length $X$ is completely immersed in a liquid of density $\rho_L$. The top face of the cylinder lies at a depth $H$ beneath the liquid surface, as illustrated. The acceleration of free fall is $g$. Which expression gives the magnitude of the upthrust force acting on the cylinder?

Density and pressure

A ball falls onto a horizontal surface and rebounds elastically. During the very brief interval when it is touching the surface, what happens to the ball's kinetic energy?

Energy conservation

A gas inside a cylinder is given thermal energy $q$. As the gas expands at constant pressure $p$ from volume $V_0$ to volume $V_F$, it does useful work, as shown. Which expression gives the efficiency of this process?

Energy conservation

An object with mass $0.30\,\text{kg}$ is projected straight upwards from the ground at an initial speed of $8.0\,\text{m s}^{-1}$. It attains a greatest height of $1.9\,\text{m}$. How much work is done against air resistance as the object rises to its greatest height?

Energy conservation

A water pump lifts a mass of $27 \times 10^3\,\text{kg}$ of water by a vertical height of $80\,\text{m}$ over a period of $1.0\,\text{hour}$. Calculate the average useful output power of the pump.

Energy conservation

Which unit is not an SI base unit?

SI units

A platform is supported by four steel wires. Each wire is $5.0\,\text{m}$ in length and has a diameter of $3.0\,\text{mm}$. The Young modulus of steel is $2.1 \times 10^{11}\,\text{Pa}$. The wires obey Hooke’s law when a load with mass $200\,\text{kg}$ is placed on the platform. Determine the amount by which the platform drops due to the extension of the wires?

Stress and strain

A tensile force of $7.00\,\text{MN}$ is exerted on a steel sample. As a result, the sample increases in length by $5.00\,\text{mm}$ along the line of the force. The sample obeys Hooke’s law. What amount of work is done in extending the sample?

Stress and strain

Two waves $X$ and $Y$ have equal frequency. The amplitude of $X$ is $1.5A_0$, while the amplitude of $Y$ is $2.5A_0$. They arrive at the same point and combine by superposition to produce a resultant wave. For this resultant wave, what is the ratio $\frac{\text{maximum possible intensity}}{\text{minimum possible intensity}}$?

Interference

A displacement-time graph for an air particle lying in the path of a sound wave is shown. Which property of the sound wave must be increasing?

Progressive waves

The sound wave appears on the screen of a cathode-ray oscilloscope (CRO), as illustrated. The CRO time-base is adjusted to $2.5\,\text{ms cm}^{-1}$. What is the frequency of this sound wave?

Progressive waves

A train horn produces sound at frequency $f_1$. As the horn continues to sound, the train travels straight towards a person at rest. The train's speed is $0.20v$, where $v$ denotes the speed of sound. The frequency of the sound received by the person is $f_2$. What is the ratio $\frac{f_1}{f_2}$?

Doppler effect for sound waves

Two satellites orbiting the Earth stay a fixed $100\,\text{km}$ apart. Satellite X sends a microwave pulse to satellite Y. The pulse needs time $T$ to arrive at Y. Satellite Y then sends a pulse of visible light back to satellite X. How long does the light pulse take to reach X?

Electromagnetic spectrum

A stationary wave is produced on a stretched string. The diagram shows the string at one moment when its displacement is greatest. The wave has a frequency of $250\,\text{Hz}$. Point P on the string has a vertical displacement of $-1.0\,\text{mm}$. What will be the vertical displacement of point P after $5.0\,\text{ms}$?

Stationary waves

What does the term diffraction mean?

Diffraction

In a dim room, a small red-light source shines onto two slits that are $0.75\,\text{mm}$ apart. Several metres beyond the slits, the light reaches a screen and produces a pattern of equally spaced bright fringes. Which change would make the spacing between the bright fringes on the screen smaller?

Interference

Which pair of quantities are both vector quantities?

Scalars and vectors

A diffraction grating is illuminated normally by light with wavelength $5.30 \times 10^{-7}\,\text{m}$. The first-order maximum is seen at an angle of $15.4^\circ$ to the direction of the incident light. What is the angle between the first-order and second-order diffraction maxima?

The diffraction grating

A particle is at rest in an electric field. The electric field is the only force acting on the particle. For which situation is the electric field strength $5.0 \times 10^{5}\,\text{V m}^{-1}$?

Potential difference and power

A fixed potential difference is maintained across two horizontal metal plates. An electrically charged oil droplet is balanced and remains still in the electric field between the plates. When part of the oil evaporates, the droplet’s mass decreases and it begins to accelerate. Its charge stays unchanged. In what direction will the droplet accelerate, and what alteration must be made to the plate spacing to prevent this acceleration?

Potential difference and power

Two resistors $R_1$ and $R_2$ are constructed from wire of the same material. They are joined in parallel in a circuit, as shown. The diameter of $R_2$ is half that of $R_1$. The resistance of $R_2$ is three times that of $R_1$. What is the value of the ratio $\dfrac{\text{average drift speed of free electrons in } R_1}{\text{average drift speed of free electrons in } R_2}$?

Electric current

A student defines potential difference as the energy transferred per unit charge. Which statement about that energy transfer is correct?

Potential difference and power

A metal cube has a resistance of $4.0\,\Omega$ measured across opposite faces. Ten of these cubes are joined to form a cuboid of $1 \times 2 \times 5$ cubes. No additional resistance is present at the surfaces where the cubes are in contact. What is the resistance of the cuboid when it is connected between faces X and Y?

Resistance and resistivity

A cell is linked to a fixed resistor. As time passes over a long interval, the internal resistance of the cell rises. How does this increase in internal resistance affect the electromotive force (e.m.f.) of the cell and the power dissipated in the fixed resistor?

Practical circuits

A circuit contains four identical resistors connected as illustrated. The battery has negligible internal resistance and an e.m.f. of $30\,\text{V}$. What is the potential difference between points X and Y?

Potential dividers

A power supply and a solar cell are being compared with the potentiometer circuit illustrated. The potentiometer wire PQ is $100.0\,\text{cm}$ in length and its resistance is $5.00\,\Omega$. The power supply has an e.m.f. of $2.000\,\text{V}$, whereas the solar cell has an e.m.f. of $5.00\,\text{mV}$. What value of resistance $R$ should be chosen so that the galvanometer gives a zero reading when PS $= 40.0\,\text{cm}$?

Potential dividers

The table shows information for four nuclei, $P$, $Q$, $R$ and $S$. Which pair of nuclei are isotopes of one another?

Atoms, nuclei and radiation

A calibration curve is provided for an ammeter with an inaccurate scale. At two different points in an experiment, the meter gives readings of $0.13\,\text{mA}$ and $0.47\,\text{mA}$. What was the actual increase in current between these two readings?

Practical circuits

Which particle is classified as a fundamental particle?

Fundamental particles

A student records the length $l$ and the oscillation period $T$ for a simple pendulum. He then applies the equation below to determine the acceleration of free fall $g$. $T = 2\pi\sqrt{\frac{l}{g}}$ The measurements are given as: $l = (87.3 \pm 0.2)\,\text{cm}$ $T = (1.9 \pm 0.05)\,\text{s}$ What percentage uncertainty is there in his calculated value of $g$?

Errors and uncertainties

An object travels along a straight line. The graph illustrates how the object's velocity $v$ changes with time $t$. When $t = 0$, the object is at point X. What is the displacement of the object from point X at time $t = 0.80\,\text{s}$?

Non-uniform motion

An object starts from rest and accelerates uniformly until its speed reaches $v$. It then continues at the constant speed $v$ for $8.0\,\text{s}$ before it decelerates uniformly to rest. The overall time taken is $12.0\,\text{s}$, and the total distance covered is $60\,\text{m}$. Calculate the speed $v$.

Equations of motion

A paint-spraying device is made of a box whose axes are horizontal and vertical. Small holes are cut in one of its vertical sides. Paint is supplied to the box under pressure through a vertical tube and then leaves through the holes as thin jets travelling horizontally. The paint leaves at a speed of $2.5\,\text{m s}^{-1}$ through $400$ holes, each with an area of $0.4\,\text{mm}^2$. The density of the paint is $900\,\text{kg m}^{-3}$. Determine the horizontal force needed to keep the device at rest while the paint is being ejected.

Momentum and Newton's laws of motion

An air-filled party balloon is kept motionless several metres above the ground. The balloon is then released in still air. Which statement best describes how the balloon moves from the instant it is released until just before it reaches the floor?

Equations of motion